Does a NYY or NYM cable affects a CAT6 cables transmission if they are crossed?
It depends on the quality of the CAT6 cable. Industrial cables have larger cross section and very thick shield, also two layer shield. It is a common practice to place the signal cables on one side and power cables to the other side of the tray. If you put a separator is yet better, the best would be separate trays.
If the cables go underground, you should have also two separate hoses. 

It is almost inevitable to cross the power cables at certain section. Try to lay 
the CAT6 as distant as possible from power, even when you cross it.