Triangle ABC has a right angle at C, AC=3 and BC=4. Triangle ABD has a right angle at A and AD=12. Points C and D are on opposite sides of AB. The line through D parallel to AC meets CB extended at E. If DBDE=nm, where m and n are relatively prime positive integers, then m+n=
[asy]
size(170);
defaultpen(fontsize(10pt)+linewidth(.8pt));
pair C=origin, A=(0,3), B=(4,0), D=(7.2,12.6), E=(7.2,0);
draw(A--C--B--A--D--B--E--D);
label("A",A,W);
label("B",B,S);
label("C",C,SW);
label("D",D,NE);
label("E",E,SE);
[/asy]
<spanclass=′latex−bold′>(A)</span>25<spanclass=′latex−bold′>(B)</span>128<spanclass=′latex−bold′>(C)</span>153<spanclass=′latex−bold′>(D)</span>243<spanclass=′latex−bold′>(E)</span>256