Find the sum of the $x$-coordinates of all possible positive integer solutions to $\frac1x+\frac1y=\frac17$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the sum of the $x$-coordinates of all possible positive integer solutions to $\frac1x+\frac1y=\frac17$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
78
Find the sum of the $x$-coordinates of all possible positive integer solutions to $\frac1x+\frac1y=\frac17$.
train