Migrating Plesk mySQL Files to cPanel

Due to a RAID failure that was imminent on a Plesk server that we're dumping anyway I had to copy all html directory files/folders to the new server. I wrote a script that easily deposited the files into each directory. It just dawned on me that I have to chown root to the admin name. But I also moved the mysql files from the failing server to the new server. One trick with Plesk was that we could just copy the mysql files to a new server. No hiccups. But can I do this with cPanel or are the database names held in a database? I don't want to corrupt anything. I don't know if I can create a master dump file of mySQL files outside of /var/lib/mysql and then recreate the database through cPanel and then restore. /var/lib/mysql. But then there's /var/lib/mysql-files/. Confused. Do I create the database in the customer domain and then restore from a dump file (if I can make one?) Or can I just copy them in like on a Plesk sever? I hate Plesk with a passion! ARG!!! We have a lot of servers to migrate. If I can just copy them I can add the command to the script I wrote. How would you advise me? I don't want to create a support issue by doing it wrong.