We report Plateau de Bure Interferometer ( PdBI ) 1.1 mm continuum imaging towards two extremely red H - [ 4.5 ] > 4 ( AB ) galaxies at z > 3 , which we have previously discovered making use of Spitzer SEDS and Hubble Space Telescope CANDELS ultra-deep images of the Ultra Deep Survey field . One of our objects is detected on the PdBI map with a 4.3 \sigma significance , corresponding to S _ { \nu } ( 1.1 mm ) = 0.78 \pm 0.18 mJy . By combining this detection with the Spitzer 8 and 24 \mu m photometry for this source , and SCUBA2 flux density upper limits , we infer that this galaxy is a composite active galactic nucleus/star-forming system . The infrared ( IR ) -derived star formation rate is SFR \approx 200 \pm 100 M _ { \odot } / yr , which implies that this galaxy is a higher-redshift analogue of the ordinary ultra-luminous infrared galaxies more commonly found at z \sim 2 - 3 . In the field of the other target , we find a tentative 3.1 \sigma detection on the PdBI 1.1 mm map , but 3.7 arcsec away of our target position , so it likely corresponds to a different object . In spite of the lower significance , the PdBI detection is supported by a close SCUBA2 3.3 \sigma detection . No counterpart is found on either the deep SEDS or CANDELS maps , so , if real , the PdBI source could be similar in nature to the sub-millimetre source GN10 . We conclude that the analysis of ultra-deep near- and mid-IR images offers an efficient , alternative route to discover new sites of powerful star formation activity at high redshifts .