Yes, the SATA cable likely needs replacing. Apple had a hard time between Intel’s chip problems as well as getting a good cable made. When the 2011 system came out the system was limited to SATA II (3.0Gbps) drives. Later, Apple updated the system firmware to allow SATA III (6.0Gbps) drives as the drives where still on the slow side the cable issues didn’t show up.
After a bit of time passing… SSD drives came out and over time the performance of the drives are now hitting the performance ceiling of SATA III, sadly that’s why the drive is not working as expected. A newer rev of the SATA cable should resolve your issues but be careful as the sharp bending of the cable will cause signal issues! You want smooth bends, no sharp bends in the cable.
Here’s the needed part MacBook Pro 13" Unibody (Early 2011-Late 2011) Hard Drive Cable
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The SSD should be formatted to Mac Extended Journaled with GUID Partition Map.
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