Matrices are your friends.

Algebra Level 5

\[\large C = \begin{bmatrix} -1 & 4 \\ -3 & 7 \end{bmatrix}\]

It is given that the multiplicative inverse of \( 6C - 5I\) can be expressed as below, where \(k\), \(m\), and \(n\) are positive integers, and \(I\) is the identity matrix.

\[ \large \frac{1}{k} {(C - nI)}^{m} \]

What is \(k + m + n + 3\)?

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