If you're lucky, it's just the connector that is damaged. This is a straightforward repair if you have good soldering skills or you can have it done by a micro-solderer. Sometimes however, the damage is more on the controller/NAND side of things. You may have cracked pads or traces or even cracked solder balls if the NAND is mounted in a BGA package. This is a more serious repair and best left to an experienced micro-solderer.
Finally, you may have physically damage the circuit board to the point where the only way to get the data is via transplant (requires an identical board, not just the outer housing and model number) or chip-off data recovery. You can't just wing it as mixing the wrong controller with the NAND can scramble the data forever. This is best left to professionals.