Grate sweet potatoes and russet potato into a bowl using small holes of a box grater. Pat potatoes dry with paper towels. Stir together grated potatoes, goat cheese, flour, onion, table salt, and black pepper until well blended. Divide mixture into 4 equal portions; shape each portion into a 12- x 1-inch log. Wrap both portions in plastic wrap, and freeze 30 minutes or until slightly firm. Unwrap dough, and cut each dough log into about 15 (3/4-inch-thick) slices. Heat vegetable oil in a heavy saucepan over medium-low heat to 330°. Fry potato slices, in batches, 3 to 5 minutes or until golden and crisp. Drain on paper towels. Immediately sprinkle potato tots with fine sea salt.