$\sqrt[3]{250}=\sqrt[3]{125\cdot 2}=\sqrt[3]{125}\cdot \sqrt[3]{2}=5\sqrt[3]{2}$
$\sqrt[3]{54}=\sqrt[3]{27\cdot 2}=\sqrt[3]{27}\cdot \sqrt[3]{2}=3\sqrt[3]{2}$

$\frac{\sqrt[3]{250}+\sqrt[3]{54}}{\sqrt[3]{250}-\sqrt[3]{54}}=\frac{5\sqrt[3]{2}+3\sqrt[3]{2}}{5\sqrt[3]{2}-3\sqrt[3]{2}}=\frac{8\sqrt[3]{2}}{2\sqrt[3]{2}}=\frac{8}{2}=4$