If \( A \) is a square matrix of order 3 and \( |A| = 6 \),
it is given that
\[
\left| \text{adj} \left( 3 \, \text{adj} \left( A^2 \, \text{adj} (2A) \right) \right) \right| = 2^m \cdot 3^n
\]
where \( m \) and \( n \) are natural numbers. Then find \( m + n \).
Here, \( \text{adj}(X) \) denotes the adjoint of matrix \( X \), and \( |X| \) denotes the determinant of matrix \( X \).