MySQL completely uninstalled and reinstall but database still exists on Ubuntu 12.04

I need to completely remove MySQL all databases and installation and reinstall, because root is broken. I followed this instructions:

sudo apt-get remove --purge mysql-server mysql-client mysql-common
sudo apt-get autoremove
sudo apt-get autoclean

But when I install again with

sudo apt-get install mysql-server

Old databases, old users table with broken users, etc.. are here, so it doesn't completely uninstall/repair.

Add

rm -rf /var/lib/mysql
rm -rf /etc/mysql*

before the install to delete everything, but be careful you can have third parties schemas there like phpmyadmin,... So consider deleting one by one subfolder.

Maybe there is an elegant way of doing this, like mysql_secure_installation