Can I use a 15w LED bulb in a fixture that says max 40w incandescent or 11w CFL?
I would be willing to bet you are all set. but, err on the side of caution, and do not exceed the 11W for the base of the socket.

CFL's generate a lot of heat in the base, so its a better measure of that socket's rating to compare the heat the LED bulb generates to that fixture.

An incandescent generates most heat at the filament, which is not centrally located in the base of the bulb, unlike a CFL.

This is why you see many cooked CFL's. Here is a comparison chart to relay the idea (thanks Google and Milwaukee):


Another goodie from Google: