Solubility comparison of hexan-1-ol and cyclohexanol in water
In general is very difficult to predict solvatation some experimental models are used such as Abraham solvation equation.
I suppose that the mistake you have done is the fact that you haven't consider one of the most important factor: the molecule structure.

In this case you are comparing a cyclic compound with a linear one, if you could have a look to the potential surface of the two molecules you will see something like this:

What makes the alchol soluble is the hydrophilic hydroxyl group while the lipophilic chain is not. The  ratio between idrophilic and lipophilic area is greater in the cyclohexanol compared to 1-hexanol.