My monitor has a "Standard" preset, which is quite close to 6500K but I have often felt that it has the subtlest green cast.
This can be changed with software.. but if you don't have a calibrator or software like f.lux, you do have 1 more option available to you.. most monitors have a user preset that allows you to set your own # for the R G B values.
In my sRGB monitor, the range is 0-100 for each, and RGB values are 0-255. Need to convert.
6500K @ 10 degree angle, the RGB values are 255 249 253. To convert to 0-100, you take the # and divide it by 2.55 and round. So, 100 98 99 are the new converted values.
All of a sudden, it looks subtly more comfortable for me, and you can see this by switching back and forth between the new preset and the standard setting with a high-resolution photograph (which are standardized at 6500K if sRGB colour profile).
I wish my monitor had more than 1 customizable preset.