High Order Matrix

Matrix $\textbf A$ is given by $\textbf A= \begin{bmatrix} 6 & 11 \\ 2 & 4 \end{bmatrix}$ . If the determinant $\begin{vmatrix} \textbf A^{ 2005 }-{ 6 } \textbf A^{ 2004 }\end{vmatrix} = \left( -\alpha \right) { \beta }^{ \gamma }$ , find the value of $\alpha + \beta +\gamma.$

Where $\alpha$ , $\beta$ , $\gamma$ are integers and $\alpha$ and $\beta$ are prime numbers