Not sure if you still need help with this one, since it's been more than a year. Try putting this in your blade file.
<form action="{{ route('store') }}" method="POST">
I've had a similar problem with my code. My original form had this, at the very beginning (using default documentation code here):
<form action="{{ route('photo.store') }}>
which, after trying it out, didn't work as I would expect - nothing was being stored. After making sure that the rest of the code was OK, one of my colleagues suggested that I type in the method type, since the default method is GET, and you need the POST method for storing.