In that case, your best bet would be to just pull it upwards (away from the motherboard) and wiggle it back and forth slightly. (along the length/pci-e slot direction)
the wiggling movement does not need to be big but it kind of helps since according to physics pulling whole card at a force and pulling only one side of card results in bigger force.
just keep the wiggle movement quite small since there is not much free "space" in the pci-e slot.
Edit: above is posted based on the assumption that the retention/locking mechanism for the card was outside the actual card slot.
If it was similar to what most memory slots use (small plastic thing that kind of pushes the stick out if pressed) and it is completely broken, then there is nothing inside the slot that would keep the card there forcibly. In which case wiggle and force is pretty much best bet in my opinion. (and I've done so before with both parts working afterwards, mileage may of course wary)