... You might want to look at what is causing the 'conditions' under which the mildew/mold is growing. There are 2 main conditions for this - temperature and humidity. If you vary just one of them enough, your problem may go away.
If you have trees that block out sun or prevent airflow near the area that has the problem, trim or remove the branches. You need to permit any moisture from 'hanging around' too long on the roof. No branches should over-hang the roof's eaves line. And the roof should be able to get at least an hour's sun at some point during the day. Again, look to the trees as the 'cause' of your problem.
If a portion of the house or another building is 'shading' your problem area, you may need to get more drastic. Do what you can to INCREASE airflow to the area. REMOVE trees if necessary. If the sun can't get to the area, by allowing more airflow just might help.
As for the 'mix' to clean the roof, start with 1 cup of Bleach per 1 gallon of water. This is a minimum. You can increase it a cup at a time. Just be conscious of vegetation below or at the opening to your downspouts. (Bleach DOES kill. Otherwise, you wouldn't use it on the mildew, eh?) My best to ya and hope this helps.