11MB is small.. very very small.
phpmyadmin is a nice tool, but it's complete crap when it comes to dumping and uploading.
Use the normal mysql commandline tools.
You can either upload the database with ftp and then load it into mysql on the server, or connect to the mysql server directly from your local mysqlm, something like this:
mysql databasename -hremotehost -uremoteuser -premotepassword < mysqldump databasename -hlocalhost -ulocaluser -plocalpassword --opt