/usr/include/gtk-3.0/gdk/x11/ is in libgtk-3-dev 3.10.8-0ubuntu1.4.
This file is owned by root:root, with mode 0o755.
..
/usr/include/gtk-3.0/gdk/x11/gdkx11applaunchcontext.h
/usr/include/gtk-3.0/gdk/x11/gdkx11cursor.h
/usr/include/gtk-3.0/gdk/x11/gdkx11device-core.h
/usr/include/gtk-3.0/gdk/x11/gdkx11device-xi2.h
/usr/include/gtk-3.0/gdk/x11/gdkx11device.h
/usr/include/gtk-3.0/gdk/x11/gdkx11devicemanager-core.h
/usr/include/gtk-3.0/gdk/x11/gdkx11devicemanager-xi2.h
/usr/include/gtk-3.0/gdk/x11/gdkx11devicemanager.h
/usr/include/gtk-3.0/gdk/x11/gdkx11display.h
/usr/include/gtk-3.0/gdk/x11/gdkx11displaymanager.h
/usr/include/gtk-3.0/gdk/x11/gdkx11dnd.h
/usr/include/gtk-3.0/gdk/x11/gdkx11keys.h
/usr/include/gtk-3.0/gdk/x11/gdkx11property.h
/usr/include/gtk-3.0/gdk/x11/gdkx11screen.h
/usr/include/gtk-3.0/gdk/x11/gdkx11selection.h
/usr/include/gtk-3.0/gdk/x11/gdkx11utils.h
/usr/include/gtk-3.0/gdk/x11/gdkx11visual.h
/usr/include/gtk-3.0/gdk/x11/gdkx11window.h