1. Uninstall your previous version.
sudo apt-get remove --purge openoffice.org-* rm -rf /home/[yourUsername]/.openoffice.org
2. Of course, download OpenOffice 3.1 first (in my case 'OOo_3.1.0_LinuxIntel_install_en-US_deb.tar.gz').
Download Link
3. Next, launch the terminal and extract the package.
tar -xvzf OOo_3.1.0_LinuxIntel_install_en-US_deb.tar.gz
4. Now, enter to its directory by issuing the following commands.
cd OOO310_m11_native_packed-4_en-US.9399/DEBS/
5. Install all the packages inside.
sudo dpkg -i *.deb
6. Next, install the shortcuts.
cd desktop-integration sudo dpkg -i *.deb
7. Now you should have OpenOffice ready in your menu.
These are the steps I made for me to complete my installation without conflict. Of course there are other methods like from the repository, but yesterday when I installed mine, the update was still not uploaded. Also, you may notice that the splash screen is still on OpenOffice 3.0, its normal, maybe the just forgot to change it.