Transferring data with busted IPhone screen

I searched and didn't see any relevant results, but has anyone found a work around for getting data off an IPhone with a broken screen? The device has power and is recognized by the computer. If you connect to ITunes it requires you to unlock your phone, but that's impossible without a functioning screen. I backup pretty regularly, but I had some recent family photos and videos that may be lost if I don't find a solution.