8. Solve the equation $\sqrt[3]{x+2}+\sqrt[3]{3 x-1}=\sqrt[3]{16 x+4}$. In the answer, specify the root if there is only one, and the sum of the roots if there are several.
Answer: 1.25

Solution: Let $a=\sqrt[3]{x+2}, b=\sqrt[3]{3 x-1}$.

Then $a+b=\sqrt[3]{4\left(a^{3}+b^{3}\right)}$. Raising both sides to the cube, we get $(a+b)^{3}=4\left(a^{3}+b^{3}\right)$. Moving to one side and factoring, we have $(a+b)(a-b)^{2}=0$.

Therefore, either $a+b=0$, in which case $x+2=1-3 x$, leading to $x=-0.25$, or $a-b=0$, in which case $x+2=3 x-1$, i.e., $x=1.5$.