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:
$$x^3+35-x^3+3x \sqrt[3]{35-x^3}(x+\sqrt[3]{35-x^3})=35+3\cdot30 $$
$$(x+\sqrt[3]{35-x^3})^3=5^3$$
Assuming  $x$  to be real, $$x+\sqrt[3]{35-x^3}=5\iff\sqrt[3]{35-x^3}=5-x$$
Take cube in both sides
