To obtain a private helicopter add-on rating, what you're really doing is adding an additional catagory and class to your existing private pilot certificate.
As such, some things are required, some are not. You do not have to take another written test, but you do have to meet all the requirements of 61.109(c), which does include cross country flights.
The very least amount of flight time it can be done in is 30 hours, 20 of which must be dual, 10 of which must be solo. I've seen people do it pretty close to those numbers, but only when taking it on full time.