If you want a cheap one you can keep nearby, the only thing I can think of is a temporary mob grinder. Just build a platform high enough in the sky so you won't trigger spawns on the surface or underground and put a mob grinder there. Then just climb up (if you link two nether portals that close it'd be even faster), let the mobs spawn, and kill them for XP.
If you do that, just be sure none of them can see you or the killing chamber is made of bedrock obsidian. It'd be terrible if a creeper spawned and blew it up.
A fast rate of mob kills will need a fast rate of mob spawning.
A fast rate of mob spawning will need a large dark-surface area.
A large dark-surface area will involve placing a lot of blocks.
Placing a lot of blocks will involve substantial time spent.
A common mob will drop 5 exp when killed. Mending restores 2 durability for every exp point. Assuming the OP isn't wearing anything else, that means 150 kills for full restoration. A simple mob grinder stacked up a few times should work fine.
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Watch out for the crabocalypse. Some say the day will never come. But it will.
If you'd like to talk with me about other games, here are a few I play.
Team Fortress 2
Elder Scrolls series
Left 4 Dead 2
Dead Rising series
7 Days to Die
Just Cause series
Come to think of it, I mainly play fighting-based games.
If you don't mind some major cheatiness, set up a sand duplicator and smelt the creation into glass. In 1.13 you can attach this to an autosmelter array (furnaces remember the total exp from smelted items since the last time a player pulled output items from the furnace) and if you don't want to keep the glass you can attach the output hopper to an old-fashioned incinerator. You'll need to provide the fuel, though.
If you are in a 1.14 snapshot, you can set up an automatic bamboo farm. Bamboo can be used as furnace fuel (it sounds like it's not very good), and it's the fastest-growing plant in the game. By sheer quantity, you could probably keep the furnaces smelting for the entire 15 minutes for continuous maximum xp generation.