$SU(2)_L$-invariance links charged dilepton $\bar q\,q^\prime\,\ell^+\,\ell^-$ and dineutrino $\bar q\, q^\prime\, \bar\nu\,\nu$ couplings. This connection can be established using the Standard Model Effective Field Theory framework, and allows to perform complementary experimental tests of lepton universality and charged lepton flavor conservation with flavor-summed dineutrino observables. We present its phenomenological implications for the branching ratios of rare charm decays $c\to u\,\nu\,\bar\nu$ and rare $B$ decays $b\to s\,\bar\nu\,\nu$ decays.