As one that has worked many years in the print industry doing high end color work, you might consider a more reliable approach.
We learned early on that monitor calibration, even with the highest quality monitors and calibration equipment, remained elusive. I remember one nightmare set of days with 12 monitors all connected to a single output and trying to get them all the same.
When assessing an image's color values, always go by the numbers in sampling. In Photoshop, the Info box is the target here. Constantly hover the mouse over areas, look as the values. Depending on whether you're doing it for print to RGB display, the gamut you use will vary. Generally speaking, you can color calibrate any image by:
Check absolute black and white point, make sure they are balanced (Black - 0/0/0 or 0/0/0/0 CMYK, white 255/255/255 85/83/83/95 CMYK, will vary depending on undercolor removal settings but CMY should be balanced)
Most important, target gray areas. Gray areas will tell you the overall balance of the image and can eliminate casts. For example, an area that is supposed to be gray will read 45/42/42/50, if it reads 50/42/42/50, you know you have a bluish cast. (Cyan is always SLIGHTLY higher than M and Y, due to color contamination and the tinting strength of C versus Y and M.)
Target important colors and their chroma: a good red will read <10/100/80/0, a dirty one will have high percentages of Cyan.
In time, you will learn to use the same method to test 3/4 tones, midtones, and 1/4 tones as well, just by the numbers.
Both RGB and CMYK gamuts appear in Photoshop's color sampling. Which you will use depends on what you're most comfortable with. For the most part, CMYK is more intuitive for most people because we've learned subtractive color since kindergarten and know that red + blue = orange - which is not the case with RGB (additive) color.
It takes a lot of time to become comfortable with this approach, but the best choice for color - don't rely on a monitor at all. The groundwork is constantly shifting and for the most part an unknown value.