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Burchill has been recovering from a tight groin whilst midfielder Cummins has had a badly bruised foot carried over from last season.
Both men are now in contention to push for a starting role in Mark Robins' side for this weekend's home game against struggling Chester City.
Marcus Haber, a Canadian under-20 International, did not figure due to clearance of his paperwork coming through.
Trialist Oliver Hotchkiss, a product of the Leeds youth academy, played a part in proceedings along with new striker Drewe Broughton who signed a month's contract last Friday.