So, installing vim-enhanced and vim-X11 is enough, but is not at the same time. To enable the system functions like +clipboard, you moreover need to use the vimx executable rather than vim or vi (even though they are probably identical, the name changes the behaviour).

One way how to do that permanently is by adding aliases in your .bashrc file:

alias vi='vimx'
alias vim='vimx'

The complete list of features that get enabled this way is: +balloon_eval, +browse, +clientserver, +clipboard, +dnd, +mouseshape, +toolbar, +X11, +xim, +xsmp_interact, +xterm_clipboard, +xpm.

However, some of them are probably irrelevant for the terminal version of vimx and only do something for GVim.

— How do I get +clipboard support in Fedora 20?