Your motherboard has an H110 chipset (not "1150 chipset") which has an LGA1151 socket. This H110 (as well as B150, H170, Z170) supports 6th-gen Skylake CPUs out-of-the-box. Other motherboards with LGA1151 sockets are the B250, H270, and Z270, which supports both 6th-gen Skylake and 7th-gen Kaby Lake CPUs out-of-the-box.
Note that the LGA1150 sockets (you mentioned in your question) are for older 4th-gen Haswell CPU's that fits in B85, H81, H87, H97, Z87, and Z97-chipset motherboards.
The Intel i5-6600K, a 6th-gen Skylake CPU will fit the H110M PRO-VHL motherboard you have. However, this particular CPU is overclockable ("K"-series), while your H110 motherboard is not. So, you are paying for something that you can't fully take advantage of (i.e., overclocking).
If you don't plan to overclock, it is better and more logical to get a non-overclockable (non-"K" CPU), such as the i5-6600. This will be a better pair with that H110M motherboard.
The i5-6600K has a base clock speed of 3.50GHz and a boost speed of 3.90GHz, non-overclocked. It also has a higher TDP of 91W.
On the other hand, the i5-6600 has a base clock speed of 3.40GHz and a boost speed of 3.90GHz (same as the i5-6600K), non-overclocked. It boasts a lower TDP (lower power consumption/heat) of just 65W.
I'd highly suggest getting the i5-6600 instead. It is LGA1151 and would work on that motherboard of yours, while saving a lot of money for the same performance you intended.