It is known that Sacks forcing does not add Cohen reals since it has the Laver property. I wonder if Cohen forcing can add a Sacks real. If $V$ is a model of ZFC, and $V[c]$ is the extension by adding one Cohen real, then in $V[c]$, is there any Sacks real over $V$?
I vaguely remember reading somewhere that the answer is no. But I can't find a source. Is there an obvious argument?