Z:gnu-www-ja-gpl-faq--9ae733-No. The X11 license is compat/en

No. The X11 license is compatible with the GPL, so you can add a module to the GPL-covered program and put it under the X11 license. But if you were to incorporate them both in a larger program, that whole would include the GPL-covered part, so it would have to be licensed as a whole under the GNU GPL.