Ballet originates from France. I think this is why is has a silent 't' at the end.
I am guessing France since all the ballet terms are french.
Ballet was originated many years ago. Most of the steps in ballet today are said in french, so I would say that ballet is french.
The Nutcracker ballet originates from Russia. Nutcrackers originate from England. Nutcrackers, the decoration, originate from Germany.