An octahedron (a solid with 8 triangular faces) has a volume of 1040. Two of the spatial diagonals intersect, and their plane of intersection contains four edges that form a cyclic quadrilateral. The third spatial diagonal is perpendicularly bisected by this plane and intersects the plane at the circumcenter of the cyclic quadrilateral. Given that the side lengths of the cyclic quadrilateral are 7,15,24,20, in counterclockwise order, the sum of the side lengths of the entire octahedron can be written in simplest form as a / b. Find a+b.