Double Cube Roots

Algebra Level 2

$\sqrt{\sqrt{\sqrt[3]{\color{#3D99F6}{64000}} + {\sqrt[3]{\color{#3D99F6}{64000} + \color{teal}{3(1640) + 1}}}}}$

With the assistance of the algebraic identity $(a+b)^3 = a^3 + b^3 + 3ab(a+b)$ , evaluate the above expression.