It's pretty weird, seeing that HDD's are recognisable, and that SSD works when in an enclosure (Crucial M500).
I've read somewhere that it could be an issue with the cable, but I bought a replacement cable, and it doesn't recognise the SSD either.
One idea that I have might be the issue is that the SSD needs 1.7 A of current, while the HDD I tested it with only 1 A.
Best Answer
The actual problem here was that I installed the OS while the SSD was in an external enclosure, not installed in the internal bay. When I wiped the drive, installed it in the bay and then installed the OS from the old HDD, now in an external drive, my problems were solved.
I also tried another SATA cable before switching the positions, and that didn't help.