A pyramid has a square base with sides of length \(1\) and has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that one face is on the base of the pyramid and its opposite face has all its edges on the lateral faces of the pyramid. The volume of this cube can be expressed in the form \(k\sqrt{2} - m\). Please calculate the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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