In a large bowl, combine the salt, sugar, brown sugar, cumin, chili powder, black pepper, cayenne pepper and paprika and mix well. Rub brisket thoroughly with this mixture and set aside.
Build a fire in one half of a large grill. For best results, use an aromatic wood such as mesquite.
When fire is ready, place brisket on grill, making sure that it is not above any part of the fire. Close grill cover and open vent about 1/2-inch.
Feeding the fire periodically, cook for 8 to 10 hours or until the internal temperature is 165º to 170ºF and the meat is very tender. The exterior of the meat should be very black.
Remove from the fire, trim off excess fat and carve against the grain into very thin slices.
Servings: 8