Let \( |A| = 6 \), where \( A \) is a \( 3 \times 3 \) matrix. If \( \left|\operatorname{adj}\!\left(3\,\operatorname{adj}\!\left(A^{2}\cdot \operatorname{adj}(2A)\right)\right)\right| = 2^{m}\cdot 3^{n} \), \( m, n \in N \), then \( m+n \) is equal to ______.
