Properties of six-quark dibaryons in nuclear medium are considered by example of $A=6$ nuclei within the three-cluster $alpha+2N$ model. Dibaryon production in nuclei leads to the appearance of a three-body force between the dibaryon and nuclear core. This non-conventional scalar force is shown to provide an additional attractive contribution to the three-body binding energy. This three-body contribution improves noticeably agreement between theoretical results and experimental data for the majority of observables. The most serious difference between the traditional $NN$-force models and the dibaryon-induced model is found for the nucleon momentum distribution, the latter model providing a strong enrichment of the high-momentum components both for $^6$Li and $^6$He cases.