Don't use superglue but yeah that's the idea behind the repair.

Get some sandpaper (around 300 grit should work fine) and stuff it up real good underneath where you'll cover it.

Then use a good glue. Maybe that clear gorilla glue for wood would work good.

Something like this is what I use: Masters Contact Cement 8oz- https://www.amazon.com/dp/B00BZXB2FI/ref=cm_sw_r_apan_i_9CV6ZRYT8DXHRJFQ3EXW

I think this is as cheap as you'll make out on this and if you take care in what your doing it'll look fine.

Or this glue (I actually think this stuff is better) Barge All-Purpose TF Cement Rubber, Leather, Wood, Glass, Metal Glue 2 oz https://www.amazon.com/dp/B00B5XDPLC/ref=cm_sw_r_apan_i_JYZYEHQ3XZQYB1878TD4?_encoding=UTF8&psc=1