들려주길 is the short form of 들려주기를, and 바래요(바라요) is often omitted.
V-기를 바라다 means "to hope that V"
바라다 is normally conjugated to 바라요 like a normal verb.
But you will almost only encounter 바래요, even if it's considered as a mistake.
I even think that 바래 is so commonly used that 바라 (the correct form) doesn't sound right to the ear anymore.