Double Cube Roots

Algebra Level 2

\[\sqrt{\sqrt{\sqrt[3]{\color{blue}{64000}} + {\sqrt[3]{\color{blue}{64000} + \color{teal}{3(1640) + 1}}}}}\]

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