  Let ${\mathcal{P}_{n}}$ denote the set of positive integers which are prime
to $n$. Let $B_{n}$ be the $n$-th Bernoulli number. For any prime $p \ge 11$
and integer $r\ge 2$, we prove that $$ \sum\limits_{\begin{smallmatrix}
  {{l}_{1}}+{{l}_{2}}+\cdots +{{l}_{6}}={{p}^{r}}
  {{l}_{1}},\cdots ,{{l}_{6}}\in {\mathcal{P}_{p}}
\end{smallmatrix}}{\frac{1}{{{l}_{1}}{{l}_{2}}{{l}_{3}}{{l}_{4}}{{l}_{5}}{l}_{6}}}\equiv
- \frac{{5!}}{18}p^{r-1}B_{p-3}^{2} \pmod{{{p}^{r}}}. $$ This extends a family
of curious congruences. We also obtain other interesting congruences involving
multiple harmonic sums and Bernoulli numbers.
