Well I have found a “trick” to solve the problem, but i do not know its limits yet.
The solution is backup the db not via phpmyadmin (in cpanel) but via Backup Wizard (in capnel).
I chose the partial backup and selected mysql db only.
The result is a compressed .sql.gz file, that compressed a ~70 MB DB to ~11 MB. And I was able to import it via usual method.
If anyone has more tricks up its sleeve, feel free to share with noobs like me 