I tried creating a computer program for this problem, and it couldn't find an answer; it would simply go in an infinite loop! Something tells me that there is no solution to this.
If you put in an answer that is possible (like 53/60), then the program finds the answer in very little at all. \(\frac{2}{6}+\frac{3}{4}-\frac{1}{5}=\frac{53}{60}\).
Anyone who wants to see it can; here's the link for those curious
It is possible that I am misinterpreting this question as well; I am assuming that the numbers listed (1-6) can only be used once. Is this a correct assumption?