Mysql and codepage problem

We use RT, and it is realy beautifull!
But we have some problems with migration. I’m not a DBA and my knowledge
of mysql isn’t good at all.
The problem in codepages. We use Russian language in tickets, and then i
do usual mysqldump from working server and trying to restore it at new
server, some letters changed to another symbols.
Why? And what i must do?

With respect,
Antony Pavlenko