Answer
Frank was wrong because he added the radicands as well as the indices of the radicals.
The correct answer is $52x\sqrt[3]{xy}$.
Work Step by Step
Frank was wrong because he added the radicands as well as the indices of the radicals.
The correct solution and answer is:
$10x\sqrt[3]{xy}+42x\sqrt[3]{xy}
\\=(10x+42x)\sqrt[3]{xy}
\\=52x\sqrt[3]{xy}$