Backup MYSQL DB on one server and restore on other, do i need the same version of MYSQL?

Backup MYSQL DB on one server and restore on other, do i need the same
version of MYSQL?

I backupped my old db on ubuntu 10.10 server using mysql 5.1.49 using
mysqldump
now I want to restore the file on my other machine, using ubuntu 12.04
server with Mysql version 5.5.32 on it. I managed to copy the files via
rsync but i can't load the DB.
I tried it with :
sudo mysql -u root -p fulldump.sql < fulldump.sql
I get this error :
ERROR 1049 (42000): Unknown database 'fulldump.sql'
BUT the name of the file is fulldump.sql and it's the folder I am
currently in of course. Any ideas ?