While the workspace of traditional ground vehicles is usually assumed to be in a 2D plane, i.e., SE(2), such an assumption may not hold when they drive at high speeds on unstructured off-road terrain: High-speed sharp turns on high-friction surfaces may lead to vehicle rollover; Turning aggressively on loose gravel or grass may violate the non-holonomic constraint and cause significant lateral sliding; Driving quickly on rugged terrain will produce extensive vibration along the vertical axis. Therefore, most offroad vehicles are currently limited to drive only at low speeds to assure vehicle stability and safety. In this work, we aim at empowering high-speed off-road vehicles with competence awareness in SE(3) so that they can reason about the consequences of taking aggressive maneuvers on different terrain with a 6-DoF forward kinodynamic model. The model is learned from visual and inertial Terrain Representation for Off-road Navigation (TRON) using multimodal, self-supervised vehicle-terrain interactions. We demonstrate the efficacy of our Competence-Aware High-Speed Off-Road (CAHSOR) navigation approach on a physical ground robot in both an autonomous navigation and a human shared-control setup and show that CAHSOR can efficiently reduce vehicle instability by 62% while only compromising 8.6% average speed with the help of TRON.