2023 AIME I Problem 13

Each face of two noncongruent parallelepipeds is a rhombus whose diagonals have lengths \sqrt{21} and \sqrt{31}. The ratio of the volume of the larger of the two polyhedra to the volume of the smaller is \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n. A parallelepiped is a solid with six parallelogram faces such as the one shown below.