Comparing Vx and Vy, Vx is the speed which gives you the best climb gradient (or flight path angle, whichever you prefer) for specific configuration (flaps) and Vy is the speed, which gives you the best rate of climb, but the climb gradient is somehow decreased compared to Vx.
Usually, the only time we use Vx is when we want to clear the obstacles, and climb gradient achieved by flying at Vy isn't sufficient. This usually happens at takeoff, initial climb, or if we have to meet published altitude constraints of a SID in IFR flight (for example, when reaching 5 DME from XYZ VOR, be at 5500ft or above). The use of Vx has its downsides, reduced forward visibility (since nose of the aircraft is pointed high up in the sky) and engine cooling. Most aircraft piston engines used in GA aircraft are air-cooled and depend on the airflow to cool the engine (mainly oil and cylinders). If we reduce the speed from Vy to Vx, the airflow reduces and it may not be sufficient to provide adequate engine cooling. Therefore, we usually climb at Vy or even higher (depends on the aircraft type and the cylinder head temperatures) so that engine temperatures remain within operational limits.
In your case, you are cruising at 6000ft and you would like to (whatever the reason), climb to 7000ft. If you have near obstacles and require steep climb gradient, you obviously fly at Vx, so you don't collide with terra firma, but usually during cross country flight, you want to climb and get somewhere at the same time, so Vy is a good compromise between ground speed, climb gradient and engine cooling. Also, usually ATC requires you to be at let's say FL100 in 5 minutes, very rarely in next 5 miles, so you use Vy to get to FL100 in the least amount of time.