First, we can rewrite the integral as:
$$
\int \frac{1}{\sqrt[3]{x}} dx = \int x^{-\frac{1}{3}} dx
$$
Now, we can use the power rule for integration, which states that:
$$
\int x^n dx = \frac{x^{n+1}}{n+1} + C
$$
Applying the power rule to our integral, we
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