Six six to the six

Algebra Level 1

\[ \large\color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} + \color{green} 6^{\color{blue} 6} = \color{green}6^ {\color{brown}a} \]

If \(\color{brown} a\) satisfies the equation above, what is the value of \(\color{brown} a\)?

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