47.3. Form an equation with integer coefficients, one of the roots of which is $\sqrt[3]{2}+\sqrt[3]{3}$.

$$
\text { (9-10 grades) }
$$
47.3. Let $x=\sqrt[3]{2}+\sqrt[3]{3}$. Cubing, we get:

$$
x^{3}=2+3 \sqrt[3]{4} \cdot \sqrt[3]{3}+3 \sqrt[3]{2} \cdot \sqrt[3]{9+3}=5+3 \sqrt[3]{6}(\sqrt[3]{2}+\sqrt[3]{3})
$$

Thus, $x^{3}=5+3 \sqrt[3]{6} \cdot x$, i.e., $\left(x^{3}-5\right)^{3}=162 x^{3}$ or finally: $x^{9}-15 x^{6}-87 x^{3}-125=0$.