With the 3.8L and 6-speed, 33s are ok. Sometimes 6th gear is almost useless, but overall you can survive it. I did this with my 2007 JK-X since I had the 4.10 gears.
35s would be completely different. You'd find 6th gear to be completely useless, and the truck would be 0-60 in hours, not minutes.

I know the auto isn't the same, but with my 2011 JKUR I already knew I'd have to regear to go 35s. I chose to go to 5.38s as I planned on 37s eventually, but I'm not regretting going to that ratio even with the 35s. It's a completely new truck this way.

I believe, with the 6-speed manual, that 5.13s are recommended for 35" tires.

 

Whoa. That's really pushing it

 

There is information in this thread that could steer you wrong. It is important to know which year the vehicle has, your 2011 has very different gearing than 2012+ with the 3.6L. Also manual and auto are very different for the 3.8L engine.

Using the gear chart that a JK Forum user created years ago is your best bet (forgot his username).
On a 2011 manual, 3.8L engine, I think you would want 4.56 unless you want lower gearing which you could do 4.88. This would be up to your driving desires, but stock rubicon would be closest to 4.56.

 

3.6L gear chart for reference or future viewers. Auto and manual are almost the same for 2012+ (3.6L) while there is a big difference in gearing on 2007-2011 (3.8L) wranglers.

 

Toyo open country R/T 285/75R18.

 

FYI, my set up...
2015 JKUR, auto trans, 35's and 4:56's. Live in so cal at approx 900' elevation. Freeway speeds 65-70 mph at just a few hundred under 3000 rpm. It goes up fairly steep freeway grades without downshifting out of OD. I am pleased with its performance with this set up, and I don't have any other perf mods... Bone stock as far as engine/exhaust goes. Hope this is of some help in your decision.

O||||||O

 

Wow. That is a massive tire for stock gears! Has to really zap the fun out of driving that!

 

3000 rpm is why I wouldn't plan on going over 4:10's. I tend to drive to much highway to put up with running that high of rpm but it going to come down to how you plan to use your rig. For me 33's and 3:73's with plans to do over landing trips I will be fine and 4:10's with 35's should be the same but if your planning to get serious off road then everything I have read and talked to folks about plan for that re-gear in time. I like running at my current 2100 rpm at 70mph

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Have a 2014 Rubi with 6spd. Kept stock 4.10s for 3 months after I lifted (2.5) and put 315/70/17s on. It was okay, but I found that 1st did not have a lot of grunt and that I had to shift down in 6th when hitting hills. Could have lived with it, but decided to re-gear. Got ripper deal on Yukon gears from 4ws.com (forum sponsor). Moved to 4.56. Feels like stock Rubi again. Every now and then, I wish I would have gone to 4.88 for more low end grunt, but I'd you drive at speed you are keeping revs 100-200 rpm higher sustained. Trade off. Wish the 3.6 had more torque earlier.

 

what is the intended use of your jeep?

on-highway big tires suck. you can dump a ton of money in to make it not suck. proper lift kits with correct geometry correction, gearing, etc. will be necessary. otherwise the ride experience will be bad. possible power boost with diesel conversion, or v8, or supercharge the 6 would be a bonus.

if it's for off road hell yeah! again gearing matters because with 4.10's and lots of torquing you can break stuff easier. for off road you would probably want to do full swap and keep your stock axles for when you sell the jeep.

if it's for "road show" i'd say keep your 33's or close to that. otherwise you will have something less fun to drive on the highway just to have the looks.