FGLRX (Catalyst 11.6) is it compatible with kernel 2.6.39?
There is a blog entry here which states that you have to patch the new catalyst driver to make it work with 2.6.39
Full instructions can be found in that blog together with links to the source code which need to be used to patch.
EDIT: Since the original question was for Catalyst 11.5, the question has been revised for Catalyst 11.6
This forum entry gives instructions on how to compile the patches for this new catalyst version - To complete the answer, I've reproduced the answer - note - this is for 64bit - if you are using 32bit, you'll need to change the entries for "x86_64" for the 32bit equivalents. Also you will not need to install the ia32-libs library:
sudo apt-get install -y build-essential cdbs fakeroot dh-make debhelper debconf libstdc++6 dkms libqtgui4 wget execstack libelfg0 dh-modaliases
sudo apt-get install -y ia32-libs
cd ~; mkdir catalyst11.6; cd catalyst11.6
wget http://www2.ati.com/drivers/linux/ati-driver-installer-11-6-x86.x86_64.run
wget http://www.mindwerks.net/wp-content/uploads/2011/03/2.6.39_bkl.patch
wget http://www.mindwerks.net/wp-content/uploads/2011/03/no_bkl.patch
chmod +x ati-driver-installer-11-6-x86.x86_64.run
sh ./ati-driver-installer-11-6-x86.x86_64.run --extract ati
cd ati; for i in ../*.patch; do patch -p1 < $i; done
./ati-installer.sh 8.861 --buildpkg Ubuntu/natty
cd ..
rm -rf ati
sudo dpkg -i fglrx*.deb
sudo reboot