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Really a matter of taste, if it's not specified; Dark will have a little bit more moisture, but nothing significant. Personally, I'd go for dark.
Not an answer, but ooh apple cake, could you please share the recipe?
Cynthia is a trusted source on Bread/Baking.
Dark brown sugar is going to have a higher molasses content than light, and therefore a slightly higher acid content. If using dark, perhaps bump the baking soda by 1/8 teaspoon.
Typically, if a recipe doesn’t mention which, it means light. But as other have posted it is a matter of taste.
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