We present a measurement of the top-quark mass in pp collisions at s√=1.96  TeV which uses events with an inclusive signature of missing transverse energy and jets. The event selection is sensitive to tt→W+bW−b→lνbqq′b independent of the lepton flavor and results in a large acceptance for W→τν decays. All-hadronic tt decays and events with identified electrons or muons are vetoed to provide a statistically independent sample with respect to all previous measurements. The top-quark mass is inferred from the distribution of the scalar sum of all jet transverse energies and the missing transverse energy. Using 311  pb−1 of integrated luminosity recorded by the Collider Detector at Fermilab, we measure a top-quark mass mt=172.3+10.8−9.6(stat)±10.8(syst)  GeV/c2. While the uncertainty on mt is larger than that of other measurements, the result is statistically uncorrelated with those of other methods and thus can help to reduce the overall mt uncertainty when combined with other existing measurements.