After a couple of weeks I could manage the problem. My hypothesis was right.
The kidney stone containing calcium, oxalate and carbonate was dissolved by drinking 1 to 2 liters a day of very acid isotonic drinks (gatorade, powerade, etc.). In many cases I added malic acid to the drink.
I could feel the improvement after only 2 days and the stone dissolved after few weeks.
Carbonate is alkaline and very reactive with acids. This is how the mechanism to dissolve THIS SPECIFIC TYPE OF kidney stone works.