If the cage gets stuck in the wall, all is not lost. You can still make the jump. You just have to climb onto the cage, look straight at the wall, make a small "hop" to the left (do not do a full jump), as you reach the very edge of the wall button mash jump facing forwards to the wall. Its tricky but it can be done.
I believe its a bug tied with the engine due to high framerates. Alot of people ive read opt to make a brand new save game, being stuck on this bug.
Rather than start the entire game all over again, I decided to brute force my way through this bug for a good solid hour until I perfected the jump.
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