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I have a 90s model Russian Big Muff, I accidentally snapped the output jack trying to solve a problem with the pedal, and I suspect the problem may have lied originally with the Input jack.

How do I remove the jacks from the pedal? Do I just unsolder the area below and pull them off, then shove in the new ones and resolder?

Yes. Some desoldering braid would be handy too when you're taking them out.