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If you do not have a pair of precision pliers, do not attempt to straighten the bent pins.
Instead, use a sacrificial SATA connector cable and carefully break away one half of the connector and expose the pins. Now put the two together and clamp them using binder clips or a similar clamp. Set it down on a flat surface and copy the data off the drive. Patience is key in doing this, and it will work (provided there is no additional unseen damage).