Question Blend shapes importing incorrectly in Unity - what am I doing wrong?

I have a simple plane model I made in blender that animates using shape keys (it has no modifiers on it).

I export it as an .fbx and import it into Unity. When I animate the blend shapes, it looks like this:


(edit: seems like this gif only plays on page load - hit reload to watch it again. Sorry for the inconvenience!)


It's supposed to be a book page flipping, so this is clearly wrong. Any idea what might be causing it? All help is appreciated.