Does this imply I can send ᴇᴛʜ if I have only access to ᴇᴛᴄ balance ? I don’t control the private key of this address directly : I can use it, but not access it or view it.
This is because, The ethereum went through a hardfork occured on july 20th 2016 that gave rise to Ethereum classic when a DAO attack took place. Those who had been mining ether since then have been given with the same amount Ethereum classic.
The reason you are not able to access it is because you have stayed on with ETC blockchain and not in Ethereum blockchain. Due to this reason you can use the ETH in your wallet but your wallet currency is ETC and the Blockchain is Ethereum Classic.