Find the sum of all the rational terms in the expansion of
\[(\sqrt{2} + \sqrt[3]{3})^{12}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the sum of all the rational terms in the expansion of
\[(\sqrt{2} + \sqrt[3]{3})^{12}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
66673
Find the sum of all the rational terms in the expansion of
\[(\sqrt{2} + \sqrt[3]{3})^{12}.\]
train