Let the determinant of a square matrix $A$ of order $m$ be $mn$, where $m$ and $n$ satisfy $4m + n = 22$ and $17m + 4n = 93$. If $\left|n\,\text{adj}\bigl(\text{adj}(mA)\bigr)\right| = 3^{a}\cdot 5^{b}\cdot 6^{c}$, then $a + b + c$ is equal to: