Well, I've tested this and it works

But I've made some modification for it to work

Replace the following according:
1. - /home/<something>/
2. - <the-username>
3. - <the-password>
4. - <the-db>
5. - RSUsername
6. - RSPassword
7. - change col to prem if you have premium rs acc

save the following script to filename.sh

Code: 
date=$(date +%F)
mysqldump -u <the-username>  --password=<the-password> --databases <the-db> > /home/<something>/db_$date.sql
gzip -f /home/<something>/db_$date.sql
perl "/home/<something>/perl/rsapiresume.pl" /home/<something>/db_$date.sql.gz col RSUsername RSPassword
rm /home/<something>/db_$date.sql.gz
rm /home/<something>/rsapiuploads.txt
download the RS API (http://images.rapidshare.com/software/rsapiresume.pl)

save and upload it to /home/<something>/perl

in cPanel, add a cron job

- set Common Settings : Once a day
- command: /bin/sh /home/<something>/filename.sh