Sometimes those dimensions and MAX are a bit off. I have an Antec ONE and a Hyper 212 PLUS.
Max cooler height is listed at 155mm in the specs for the case. Yet the Hyper 212 PLUS at 159mm fits with about 3mm to spare.
Are the measurements for your case too aggressive? Too conservative? Just right?
Either way, it will be very, very close. I got lucky with my combination.