Let the determinant of a square matrix \(A\) of order \(m\) be \(m-n\), where \(m\) and \(n\) satisfy \(4 m+n=22\) and \…

Let the determinant of a square matrix \(A\) of order \(m\) be \(m-n\), where \(m\) and \(n\) satisfy \(4 m+n=22\) and \(17 m+4 n=\) 93. If \(\operatorname{det}(n \operatorname{adj}(\operatorname{adj}(m A)))=3^a 5^b 6^c\). then \(a+b+c\) is equal to:

[JEE Main 2023, 15 Apr (Shift 1)]