Preheat oven to 300°F. Mix together brown sugar, granulated sugar, salt, cinnamon, cayenne pepper, and paprika in a small mixing bowl until fully combined and mixture is free of lumps.
In a separate small bowl, beat together the egg white and water with a whisk until frothy but not stiff.
Place almonds and cashews in a medium mixing bowl. Pour egg white mixture over nuts and stir to coat. Sprinkle nuts with the sugar mixture and toss until everything is evenly coated. Spread nuts in a single layer on a baking sheet fitted with a sil-pat or parchment paper. Bake for 30 minutes, stirring a few times throughout the process. Remove from oven. Nuts will harden as they cool. Once completely cool, break apart any pieces stuck together and store in a airtight container at room temperature.