Cubes inside roots?

Calculus Level 2

113+113+23+113+23+33+...+113+23+...+993\sqrt{\frac{1}{1^3}}+\sqrt{\frac{1}{1^3+2^3}}+\sqrt{\frac{1}{1^3+2^3+3^3}}+...+\sqrt{\frac{1}{1^3+2^3+...+99^3}}

What is the value of the expression above?

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