#### Answer

The solutions are $-\frac{125}{216}$ and $125$.

#### Work Step by Step

The given equation can be written as:
$6(x^{1/3})^2-25x^{1/3}-25=0$
Let $u=x^{1/3}$.
Rewrite the equation above using $u$ to obtain:
$6u^2-25u-25=0$
Factor the trinomial to obtain:
$(6u+5)(u-5)=0$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&6u+5=0 &\text{or} &u-5=0
\\&6u=-5 &\text{or} &u=5
\\&u=-\frac{5}{6} &\text{or} &u=5
\end{array}
Since $u=x^{1/3}$, then:
\begin{array}{ccc}
\\&u=-\frac{5}{6} &\text{or} &u=5
\\&x^{1/3}=-\frac{5}{6} &\text{or} &x^{1/3}=5
\\&(x^{1/3})^3=(-\frac{5}{6})^3 &\text{or} &(x^{1/3})^3=5^3
\\&x=-\frac{125}{216} &\text{or} &x=125
\end{array}
Therefore, the solutions are $-\frac{125}{216}$ and $125$.