I am running 225/65R17's on my 2011 Patriot which are a 28.5" tall and 8.85" wide tire. That is the generally accepted biggest( i.e. height and width )tire for the Patriot and Compass without problematic rubbing issues. Most people experience no rub while a few have minimal in certain situations( like me ). As Gramps told you that 18" tire size you mention is 29.1" tall( they are 9.25" wide as well )and you are probably going to have some rub( front wheels on full turn lock and rear wheels on spring mount ). Without a lift and wheel spacers I wouldn't, personally, run that size.
On my Patriot w/ those 28.5"/8.85" tires I get the slightest bit of rub on a right turn with the wheel literally cranked to full lock. Only happens in that certain situation which basically is having to crank it while pulling into a parking spot. Even then it is minimal and just the slightest release of pressure and it stops. Probably just the wheel liner is mounted slightly off on mine or something like that. Basically keep the tire diameter at or under 28.5" and keep the width under 9" and you should be fine. Exceed either and you will have rub most likely.
Your speedo will be off as well though as Gramps pointed out. 10 MPH off seems high though? Maybe though as he is taking 65 MPH. If you are really going 60 MPH you will only be going about 55-56 MPH on the speedo going up in that 18" size with no reflash.
Unfortunately you can't accurately calibrate the speedo on these vehicles. All you can do is have the dealer reflash to a different stock size. 215/65R17 is actually the largest stock size that can be used. If you reflash to that on a vehicle with 28.5" diameter tires your speedo will be off approx 2 MPH @ 60 MPH( you will be going faster than the speedo says ). On my Patriot 60 MPH is actually 61.8MPH checked with GPS. Close enough for me as I don't speed. If you reflash the speedo to the 215/65R17 size, while running the 235/60R18's, your speedo should be off approx 2.5-3 MPH @ 60 MPH. Again you will be going faster than the speedo shows. The faster you go the more the speedo will be off and vice versa( i.e. slower you go less it is off ).
A benefit of that for the vehicle owner is your odometer shows fewer miles than actual. It isn't much but over time it could add up and maybe let you squeak in under a warranty limit.
2011 Jeep Patriot