ok ,,,if that strip was glued on there originaly heres what you have to do.
with a knife blade or putty knife would be better. work it into the crack and down forcing the piece apart until it is seperated. then clean off the glue on both sides by scraper or sand papre down to clean wood. you can then glue it back into place. you need to do this because its called "wood glue".......not glue glue.
thento glue it back in place, evenly coat both pieces with elmers, or your favorite wood glue. place it in position. i would then tack it in place with a couple small finish nails so it won't slide. if you don't like the nails, leave the head up so you can remove them later.
using a couple of bar clamp that can be reversed apply firm even preasure by pressing acrossed the cupboard. you want it firm,, but not so tight it squeezes out all the glue.
if you don't have such bar clamps, you can use a couple scrap sticks of wood cut slightly longer then the gap, so they can be wedged in snugly.
leave space for a scrap of wood under the ends of the sticks to protect the cabinet.