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Such an algebra $A$ is a 3-dimensional cubic AS-regular algebra by Kirkman--Musson--Passman. Assuming $\\mathrm{gcd}\\,(n, m)=1$ and $m \\geq n$, we extend the previous results on the Hochschild cohomology of $\\nabla A$. Known cases include $(n,m) = (1,1)$ (Belmans) and $(n = 1,\\,m \\geq 2)$ (Itaba--Ueyama). 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