Agree to @Rob. I've spent fair bit amount of time to figure out this issue as well and got it concluded that Service Broker (SB) won't get along with Entity Framework 6 (mine is 6.1.1) at this stage. All unit tests (with LocalDB, actually) I created, using EF without SB, were successful but, once they are integrated with SB, they won't work.
To clarify more, SELECT statements work but INSERT, UPDATE and DELETE won't change anything.