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Try titanium backup
Come on. Go to the Play store and read up on it. Go to their website and learn. You can back up apps with their data, i.e. Angry birds. Back it up with Titanium backup and after you install a new rom, you can re-install Angry Birds and restore the data from Titanium backup.

In the new rom, install Titanium Backup from the Play store and install the game you want to restore data for. Open Titanium and touch the the menu options (3 vertical dots at the top right) > Preferences > Backup folder location. Have it detect or point it to your Titaniumbackup folder and set it as default. To restore the game data, on the main TiBu screen, now touch the rectangle with a check mark in it in upper right next to the menu dots. In the restore section 'Run' restore all apps with data. *Important* next, Deselect all and select Data only. Checkmark the app you want to restore the data and hit the checkmark in the upper right corner to restore.I read the description on the Play Store and I backed up the data for a few games but when I go to my new ROM, I don't know how to restore it.
I'm guessing you did a full wipe between roms and now you're wondering where your backups went?
If so, bad news...
Well, I have a nandroid backup from before I flashed CM10 so couldn't I flash back to stock and fix it?