70 Dart Swinger with 275/60/15 E/T drag

They will physically fit in there, but
you might have to move stuff around, and get custom wheels; not a huge deal
IIRC 275/60-15s are just about exactly 28" tall. During launch, they will move slightly forward, so you'll need a minimum of .375 inch clearance.
If your car is lowered, don't forget the hump in the top of the tub likes to get into the tire on bumps, like the ridge above the wheel arch. Stick your head in there and eyeball this stuff before you spend your money.
Some guys shim the front perches but I don't think you can get more than .25 there, unless you swap out the factory length studs.. So the next go-to is to move the entire rear end back on the springs, and make sure it stays there. Both of these will pull the driveshaft out of the trans a like amount, but in my case it was no bother.
Depending on your spring arch, you may have to re-engineer the rear shackle angles. Plus clearance the tank for shock-body clearance.
All doable solutions, for the 28s
If you already have your wheels purchased and you are particularly attached to them, them, you may have to narrow the rear end and move the springs inboard; also doable.
275s want to be on 9" or wider rims. But that may put the sidewalls into the springs. For straightline work they will fit on 8s. But to run on the street like that, you may have to drop the tire pressure down to 26 or maybe 24, for long treadlife. Then, in the turns, they may get back into the springs as the body shifts over. So slow down until you get everything clearanced just right.
It's a bit of a battle but totally doable, and to my recollection, that particular combo needs all the tire it can get, and slapper bars besides,lol.

Happy HotRodding.