Preheat broiler with oven rack in upper middle position.
Combine first 4 ingredients in a medium bowl. Divide and shape turkey mixture into 8 (2-inch) patties. Arrange patties on a baking sheet; broil 2 to 3 minutes on each side or until done.
Combine coleslaw, apple, mayonnaise, and juice in a bowl. Divide cucumber slices over bottom halves of buns. Top evenly with turkey burgers, coleslaw mixture, and top halves of buns.
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