Conclusion.
If you're higher, you can run the engine hotter. If the engine runs hotter, it produces more thrust for a given liter of kerosene. So it goes either faster or farther, all else being equal.
Of course jet engines are, inconveniently for this explanation, bolted to airframes, and airframes have wings. The altitude best for the wing isn't usually the altitude best for the engine. But we'll let that one go.