Floored Cube Roots

Calculus Level 4

\[\large \left \lfloor \dfrac{1}{\sqrt[3]{1}} + \dfrac{1}{\sqrt[3]{2}} + \dfrac{1}{\sqrt[3]{3}} + \cdots + \dfrac{1}{\sqrt[3]{2019}} \right \rfloor = \, ? \]

\[\]Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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