Darkpassenger, you did a fine looking job.
The gorilla glue should also work fine.
As has been said, the wood is thin in that area anyway, and probably dry, which lead to the crack.
But cracks are pretty common in wood furniture. And why a lot of manufacturers have switched to plastic, not including that plastic is often cheaper to make and buy too.
The glue will likely hold up fine.
About once a year though, be sure to rub it down with murphy's oil soap.
That will keep the wood clean, and give it some moisture for the wood to soak up and prolong its' life.