If all that broke was the usb head off the pcb it may be possible to re solder the 4 usb points back to the pcb, you can do this directly or you can use for wires one side attached to the pcb then attach the 4 corresponding sides to the usb head. I don't know how mission critical the data is if its important you may have to look into professional data recovery, but remember its super expensive so it may not be worth it. BTW always make backups.
