Which part did you break - the black slide itself or the small lip black lip that it catches on. If you can avoid removing the spring loaded latch it's a good thing.
If you have to remove it - slide it all the way back to the open position. Slide a thin blade (I used a 1/2 wide flexible putty knife) between the top and bottom portions. Pry up and at an angle. Watch the spring inside go flying when the top pops off. No guarantees it won't break if it's old and dried out.
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