step 1 : take a backup
mysqldump --lock-all-tables -u root -p --all-databases > dump.sql
step 2 : remove old mysql
sudo apt-get remove mysql-server
sudo apt-get autoremove
step 3 : install new version of mysql
sudo apt-get install mysql-client-5.6 mysql-client-core-5.6
sudo apt-get install mysql-server-5.6
step 4 : restore your data
mysql -u root -p < dump.sql