Backing up data of protected apps

I am using adb to backup some applications' data from my old phone to my new one. It worked fine for all apps except the one I purchased, it took me a while to figure that out since Android and its log were not showing any errors, instead it was telling me that the backup is complete and the log says: D/BackupManagerService( 2121): Full backup processing complete. D/BackupManagerService( 2121): Full backup pass complete. and the generated backup file has a size of 549B (bytes) Note: it says "Full" but it actually for a single package. After searching I now know that Google added some kind of protection in Android 4.1+ to prevent people from coping protected applications between phones. However, I am not interested in backing up the apk itself as I can download the app from Google Play Store, instead I want to backup the data so I can restore it in my new phone and not have to deal with setting the application again. Is there a way to do that without needing root access to the device? Note: the old device is Nexus 4 (5.1.1 Cyanogen + root), while the new one is Nexus 6P (6.0 stock, no root).