A positive integer $n$ is called $\textit{un-two}$ if there does not exist an ordered triple of integers $(a,b,c)$ such that exactly two of$$\dfrac{7a+b}{n},\;\dfrac{7b+c}{n},\;\dfrac{7c+a}{n}$$are integers. Find the sum of all un-two positive integers.

[i]Proposed by [b]stayhomedomath[/b][/i]