A calculus problem by Hobart Pao

Calculus Level pending

Find the volume under the surface bounded by the planes \( z=x+1, z=-x+1, z=y+1, z=-y+1 \) and above the \( xy \) plane. If the answer can be represented in the form \( \dfrac{a}{b} \), where \( a, b \) are coprime positive integers, find \( a + b \).

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