ssd

I have a MacBook Pro A1502 model, which has a fault. I need to copy some of the data from the hardisk to my new MacBook. I assumed it had a HDD and purchased a HDD/SSD adaptor cable, as simply assumed I could just take the HDD out and plug it into my USB, via the cable and would see the 2nd hard drive etc. On opening my MacBook, I realised it has a SSD hardrive.

Can anyone advise if I can still remove the SSD, plug it into an adaptor cable and connect it to my new Macbook, so I can retrieve the data from the drive? If so, what cable is needed as I can't seem to find anything on line/google etc.

TIA