Can I fit a 11.6 inch wide tire on a 10 inch rim in the stock wheel wells of my 1969 chevelle?

Yes, it should fit, if you're referring to 11.6" of section width, and not tread width. In any case, your 10 inch rims will need 5.5 inches of backspacing.

This stuff has been covered a bazillion times...use the search function.