Proper people will be along soon... from a novice, i would say if you can lift the edge up with say a fine blade, then get in some warmed pva wood glue... bottle in a bowl od warm water... to help it flow... from both sides, and down from opened end... then bind till the glue dries.
Might be a bit of residue to sand down...
depending on the rest of the neck laquer and plans, maybe clear nail varnish to stop any lift and splinters?