DS Slot 1 Game Stuck

I've been having this issue with my original DS for a while where I put a game into slot 1 and it refuses to give it up. The game is inserted the correct way, it can be read just fine, but I am able to get the cart out only about halfway until it gets jammed/stuck and won't go out any further. I've tried to nudge it out with cardstock/plastic but nothing has worked and I am afraid I am going to damage the cart if I pull to hard. Any advice or tips on how I could go about removing it?