1+ on using titebond and dowels.

It looks like it it broke along the grain. Ideally getting some wood in there where the grain is perpendicular (or at least diagonal) to the break would help keep it from re-breaking.

I'd be tempted to drill a couple of long holes, and use bamboo chopsticks as dowels. Bamboo is very dense and hard. I have cheap kids chairs repaired this way that have taken tremendous punishment.

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