Let G = (V, E) be a directed graph, with source s belonging to V, sink t belonging to V, and nonnegative edge capacities. Give a exist a polynomial time algorithm to decide whether G has a unique minimum cut (basically an s-t capacity strictly less than that of all other s-t cuts)?

I am a bit stuck, so finding minimum cut use Folkerson-Ford and then check any other s-t path? Am i missing something here?