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Preheat oven to 350°F.
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For cake, beat sugar, vegetable oil, and egg yolks in a large mixing bowl.
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Add carrots and water and mix until combined.
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Sift dry ingredients and add to the egg mixture.
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Mix well.
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Add pecans and coconut.
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In a separate bowl, beat egg whites until stiff.
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Fold stiffly beaten egg whites carefully into the batter.
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Pour batter into a greased tube pan.
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Bake for 1 1/2 hours.
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While cake is still warm, mix up icing.
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For icing, mix sugar, buttermilk, vanilla, corn syrup, and baking soda in a medium-sized saucepan.
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Bring to a boil and boil for 5 minutes.
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Icing will be very thin - really like a glaze.
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Remove cake to a serving plate.
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Punch holes in cake with an ice pick.
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Pour icing (or glaze) over cake.
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~NOTE~ If you don't have buttermilk on hand, you can place 2 tablespoons vinegar in a 1/2-cup measuring cup. Fill cup with milk and let set a few minutes before adding it to the other ingredients.