You can't pick the case by the dimensions. You have to look the maximum CPU cooler height that the case supports. With you CPU cooler, minimum CPU cooler clearance should be at least 164mm.
Also, make sure that the case supports the standard ATX MoBo.
If you want examples then my Skylake's case, Corsair 760T (full-tower), supports maximum CPU cooler height of 170mm.
Your CPU cooler will fit just nicely in there.
pcpp:
http://pcpartpicker.com/product/x3Crxr/corsair-case-cc9011073ww
Other example would be the case of my Haswell build, Gigabyte GZ-G2SGB (mid-tower) that supports maximum CPU cooler height of 150mm.
Your CPU cooler wouldn't fit in this case. Actually it does fit but you'd be unable to close the side panel.
You don't have...