I followed the instructions in this thread
and I now have the latest Android software and root on my C6506. However, my mobile data has been randomly deactivating, usually about every 6-12 hours. I go to Settings > Wireless & networks > Internet Settings and it "downloads settings", and it works again. The APN settings are all correct for my carrier, and as far as I can tell, the downloaded settings don't actually change anything. This has happened for several days now, so I don't think it's a carrier issue, and there are no issues with wi-fi, calling, or SMS.