Rationalize the denominator: $$\frac{1}{\sqrt[3]{2}+\sqrt[3]{16}}$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Rationalize the denominator: $$\frac{1}{\sqrt[3]{2}+\sqrt[3]{16}}$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{\sqrt[3]{4}}{6}
Rationalize the denominator: $$\frac{1}{\sqrt[3]{2}+\sqrt[3]{16}}$$
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