Preheat the oven to 350ºF. In the bowl of a blender place flour, sugars, cinnamon, nutmeg, baking powder, soda and mix with a fork.
Make a well in the flour and pour the oil, eggs, yolks, vanilla, almond and mix at medium speed for 2 minutes.
Add the nuts and apples and mix for 30 seconds more.
Bake for 1 hour. Allow to cool and unmold.
Place orange juice, peel and sugar in a bowl over medium high heat to dissolve. Remove from the heat and add the rum. Brush over the warm cake.
Place powdered sugar in a bowl, add the juice and mix until smooth. Drizzle over the completely cool cake. Decorate with some extra orange peel if desired.