I have edited it again (in red), to indicate what I believe the problem is actually asking for. That is, you want to determine the pairs of natural numbers {x,y} such that the expression mx+ny (where m and n are non-negative integers) fails to take exactly 65 values among the natural numbers.

There is a result stating that if x and y are coprime then the largest integer that cannot be expressed in the form mx+ny is xy–x–y. This result is apparently referred to by some people as the Chicken McNugget theorem. In more traditional circles, the number xy–x–y is known as the Frobenius number for the set {x,y}. An old result of Sylvester (quoted here) states that if x and y are coprime then the number of unattainable linear combinations of x and y is $\displaystyle \tfrac12(x-1)(y-1)$.

If we want that number to be 65 then, as you can easily see by listing all the possible factorisations of 130, the possible pairs {x,y} (with neither x nor y equal to 2) are {3,66}, {6,27} and {11,14}.