LED Lite String Question?

So I have these cool LED Xmas lite strings which have 20 LEDs and run off of 3xAA batteries. Within the battery pack, where the power switch is, is a single resistor, 5.1 ohms (green / brown / gold / gold). I want to splice on another length of 20 LEDs to the existing set but would like to run all 40 off of the original 3xAA battery configuration. Do I just divide the resistor rating in half since I doubled the load (work being done) ? The project needs to conserve space, which is why I'm not using both battery packs.