Solve irrational equation $x \sqrt[3]{35-x^3}(x+\sqrt[3]{35-x^3}) = 30$ Solve irrational equation
$$x \sqrt[3]{35-x^3}(x+\sqrt[3]{35-x^3}) = 30$$
Here is what I tried
$t^3 = 35-x^3 \implies x = \sqrt[3]{35-t^3} $
which takes me to nowhere.

Hint: Let $a=\sqrt[3]{35-x^3}$. Then you're solving $ax(a+x)=30$.
$(a+x)^3=\left(a^3+x^3\right)+3ax(a+x)=35+3\cdot 30=5^3$.
$\iff a+x=5$. Then $(5-x)x(5)=30$. Solve this quadratic equation.
