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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