First of all, I have solution on 11.10, on Ubuntu 11.10 current firefox version is 20. Probably work all versions of Ubuntu.
Download latest version of firefox archive from mozilla https://www.mozilla.org/en-US/firefox/new/
extrack on tmp or some other directory. Just use extracted directory.
Open new terminal and kill firefox
Get a root permission via
mv /usr/lib/firefox /usr/lib/firefox.old
and then go to the directory of the /usr/lib/firefox.old and make a one copy of firefox.sh to your desktop
and copy new version of firefox from tmp to lib
mv /tmp/firefox /usr/lib/firefox
and then firefox.sh paste from desktop to usr/lib/firefox
firefox.sh for a launcher from sidebar firefox icon.
If you broke the firefox open terminal
mv /usr/lib/firefox.old /usr/lib/firefox
This solution works for other integrated unsupported distribution (LibreOffice etc.)