Installing cabinet on thick sound/thermoproofing layer and concrete
Whether you like it or not, you're going to need to mount those rails into the concrete if you want the cabinet to stay on the wall. There's not much structural integrity or load bearing capacity in 1cm of plaster.
There are a variety of ways of attaching things to a concrete wall, from screws (like Tapcon™ that are specifically designed to hold in concrete), to expanding anchors.
You indicate you'd had &quot;cavity dowels&quot; recommended to you. I'm not familiar with that term, but if they're something designed for the purpose, they should do just fine. If you expect your load to be 20Kg cabinet + 50Kg of &quot;stuff&quot;, then you're only looking at 4 of these &quot;cavity dowels&quot; which doesn't seem terribly excessive to me.
You'll need to go to your local hardware store of choice, take a look at the options there and pick anchors that meet your expected load rating. It's possible that you'll find &quot;cavity dowels&quot; that are rated higher than 20Kg per fastener, so you may not need to use as many. You'll also need to select a masonry drill bit of the appropriate size for the anchors you'll be installing. Once you have those, drill the holes and insert the anchors according to the manufacturer's instructions.
Odds are good that you'll really only need 2 anchors (of whatever type) to hold your 50-70Kg load. Anchors are designed to hold a lot of weight. It's quite possible that you'll find anchors that are rated at 50Kg each which means that 2 of them (to hold the rail level) will be more than enough to support your expected weight. Again, though, you'll need to look at the packaging of the anchors you're choosing to determine which ones are appropriate.

There's another possibility (but it's probably not something you're after or you wouldn't have chosen a wall-mount cabinet). Come up with some sort of leg affair to support the majority of the cabinet's weight from below, then your anchors into the wall are simply there to keep it from tipping over.