In my paper Supercongruences involving dual sequences [Finite Fields Appl. 46(2017), 179-216], I gave a new symmetric identity which states that if $x+y=-1$ then $$\sum_{k=0}^n(-1)^k\binom xk^2\binom{y+z}{n-k}=\sum_{k=0}^n(-1)^k\binom yk^2\binom{x+z}{n-k}.$$ (See (1.17) of the paper.)

QUESTION: Is there a combinatorial proof of the above symmetric identity?