Update mysql 5.6

sudo apt-get update
sudo apt-get upgrade
sudo apt-get install mysql-server-5.6

If you have existing data in a MySql 5.5 database, it should be migrated automatically. Though it is always a good idea to make a backup before doing a major upgrade.

First make a backup of the data in your existing database:

mysqldump --lock-all-tables -u root -p --all-databases > dump.sql

Then after installing the newer version, you can restore if needed by running:

mysql -u root -p < dump.sql

For more info on migrating MySql databases, check out: