You cannot plug a USB Rock Band controller directly into an Xbox 360. The console uses a proprietary wireless protocol (2.4 GHz) and a wired Xbox 360 Controller Connector (modified USB with different pinout + security chip). Standard USB HID is not supported for gameplay.
Best Buy: Brook Universal USB Adapter (Xbox 360 version) — $25–$35, low latency, firmware updates, supports PS3/PS4/PS5/Switch controllers too.