Derived equivalences of DG algebras are not governed by their cohomology rings

Let $\mathcal{A}$ and $\mathcal{B}$ be two connected cochain DG algebra such that ${\mathcal{A}}^{\mathrm{\#}}={\mathcal{B}}^{\mathrm{\#}}$ and the cohomology rings $H(\mathcal{A})$ and $H(\mathcal{B})$ are isomorphic. We give examples to show that $\mathcal{A}$ and $\mathcal{B}$ are not necessarily derived equivalent, thereby answering to a question of Dugas.