Debian (and most Debian derived distributions) set up a special account called debian-sys-maint to perform automated administrative functions. Such functions include starting the database server, shutting down the database server and etc. The password of this account is automatically generated, it is not the same as the password of the root account in MySQL.
To further complicate matters, this password is also stored in the MySQL database. This means that when you restore a database from a dump file, you also need to restore the password of this operator. The password of this operator is stored in /etc/mysql/debian.cnf. As a result, it is a good idea to back up /etc/mysql along with the dump file, as they go hand-in-hand.