Preheat oven to 350°F. Mist a 9-by-13-inch baking dish with cooking spray. Bring a pot of salted water to a boil. Add sweet potatoes; boil until knife just pierces flesh, 20 minutes. Drain and run under cold water until cool enough to handle.
Peel and grate sweet potatoes. Core and grate apples. Toss together in a bowl. In a small bowl, whisk cider, butter, oil, brown sugar, cinnamon and flour. Stir into potato-apple mixture. Season with salt and pepper.
Spread mixture in baking dish. Cover with foil and bake until bubbly, 1 hour. Remove foil; scatter almonds over top. Bake until almonds are lightly toasted, 15 minutes.