Would one of you fine gents be able to look a date up for me? Mod 36 no dash, SN#J353***
J353XXX would be a 1976 production.
DWalt - if the serial number were a J prefix plus 5 numerical digits it would be 1969-1970 as you reported . . . but the OP's example of J plus 6 digits would make it 1975-1976.