I've always done this...
mysqldump --user=root --password=password -A > mysql_bkup.sql
Then on the other database server...
mysql --user=root --password=password < mysql_bkup.sql
YMMV, so I'd test this on a test VM machine first.
Another thing you can do is use rsync to sync the directories over to another machine...but I don't recommend this.
Since you have Red Hat, you can ask support for assistance with this