I think the copyright date on the red/white track box is 1956. The first set in my collection with the new box is a 1957 set (20325). All my 1956 (and earlier) sets seem to still have the blue/yellow box. I'm not 100% sure if this would indicate 1957 as a clear point of change, however.
EDIT: I checked a second 20325 set in my collection (the one with the 930 caboose requiring removal of screws to change the bulb) and it had the "plain" (white?) track box.