If a function $f(x) = \frac{ax^2+bx+c}{dx^2+ex+f}$ has a horizontal asymptote of $y=3$, a removable discontinuity at $x=2$, and a vertical asymptote at $x=-5$, what is the minimum possible value for the sum of the absolute values of the coefficients $|a|+|b|+|c|+|d|+|e|+|f|$ assuming they are integers with no common factor?