Ok, it seems that the nvidia driver is properly installed. It’s weird, because official Blender comes with precompiled CUDA kernels, so you do not need install CUDA Toolkit for developers. But you need install CUDA runtime library ‘libcuda’. So you should look about it:
You always do the tests with official Blender.
I also recommend discuss this in a Fedora official forum, to see if they can make this easier for the user.
Another thing, 370.28 driver is the latest driver (recently released), I have not tried it yet. So if you still can not make it work, just in case you should try with 367.44 driver (and checking that libcuda for that version of the driver has been installed)