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I run 285/35-18 Falkens on a 10.5" wide wheel. The tire sits completely flush with the wheel - zero stretch, zero bulge. If I wanted to run a 0.5" (~12mm) wider wheel I'd run a 295 (10mm wider) to get similar fitment, though I'd personally go to 305+ because I loathe stretched tires. As Trav mentioned, expect some stretch running a 275 on an 11" wide wheel, regardless of aspect ratio.
275mm is equivalent to 10.8 inches, which is damn close to the width of the rim. Unfortunately that's the measurement of the widest part of the tire sidewall, not the thread, so depending on the manufacturer and model the actual thread might be a lot narrower. Discount brand tires are known for using narrower threads to save on manufacturing costs. Check tirerack or other reputable outlets that list the actual thread width before you buy, find a brand/model with nice wide thread and it'll fit just fine.
275 will "fit"; but general rule of thumb is to run a tire tread width AT LEAST equal to width of the wheel. As noted, some tires are wider and some narrower than "advertised". The best performance comes from a tire that is 100-120% of the wheel width so the above recommendations from Mully and DocHoon make a lot of sense. Below 100% and above 120% will both "fit" but performance at the limit falls off above and below that range.
That all said, however, a 275 is a decent fitment being so close to the theoretical "ideal" tire size, particularly due to tire availability/cost. Also, going much over that may necessitate fender rolling in the rear - depends on the wheel offset.