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Between 18-24", imho. I'd take out the first 18" or so, then dig another length of the spade to loosen the soil beneath, and then add the new soil. "The Square Foot Gardener" has a good section on how to either amend the soil you have, or mix "ingredients" to make a great veggie-garden soil.
It won't help you much now, but one of the best times to dig a garden (in the NE of the US anyway) is in the late summer or fall. You don't want to dig it while it's too wet (as it often is in the spring around here), or you have the possibility of compacting the soil too much.
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