I think you need to contact Bryston before doing this. Does the manual say not to connect both? Most equipment with balanced and unbalanced inputs have the unbalanced input tapped off one side of the balanced input. When unbalanced is selected, the second signal of the balanced input is shorted to ground.
If this is the case with Bryston, and you have equipment connected to both, it may produce a very low input impedance on the tapped line. This occurs because active source component will be driving the output impedance of the other source component connected. In addition, the balanced source will be driving a short to ground if it is turned on when unbalanced input is selected on the amp. This could fry the output stage.
If this is the case with Bryston, and you have equipment connected to both, it may produce a very low input impedance on the tapped line. This occurs because active source component will be driving the output impedance of the other source component connected. In addition, the balanced source will be driving a short to ground if it is turned on when unbalanced input is selected on the amp. This could fry the output stage.