Six six to the six

Algebra

$\large\color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} = \color{#20A900}6^ {\color{#624F41}a}$

If $\color{#624F41} a$ satisfies the equation above, what is the value of $\color{#624F41} a$ ?