Triangle $ABC$ is equilateral.  Points $D$ and $E$ are the midpoints of segments $BC$ and $AC$ respectively.  $F$ is the point on segment $AB$ such that $2BF=AF$.  Let $P$ denote the intersection of $AD$ and $EF$,  The value of $EP/PF$ can be expressed as $m/n$ where $m$ and $n$ are relatively prime positive integers.  Find $m+n$.

[asy]
import olympiad;
size(150);
defaultpen(linewidth(0.7) + fontsize(11pt));
pair A = origin, B = (1,0), C = dir(60), D = (B+C)/2, E = C/2, F = 2*B/3, P = intersectionpoint(A--D,E--F);
draw(A--B--C--A--D^^E--F);
label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,N);
label("$D$",D,NE);
label("$E$",E,NW);
label("$F$",F,S);
label("$P$",P,N);
[/asy]