  Dark gamma-ray bursts (GRBs) are sources with a low optical-to-X-ray flux
ratio. Proposed explanations for this darkness are: i) the GRB is at high
redshift ii) dust in the GRB host galaxy absorbs the optical/NIR flux iii) GRBs
have an intrinsically faint afterglow emission. Within this framework, GRB
100614A and GRB 100615A are extreme. In fact, they are bright in the X-rays,
but no optical/NIR afterglow has been detected for either source, despite
several follow-up campaigns began early after the triggers. We build
optical-to-X-ray spectral energy distributions (SEDs) at the times at which the
reddest upper limits are available, and we model our SEDs with the extinction
curves of the Milky Way (MW), Small Magellanic Cloud (SMC), and the attenuation
curve obtained for a sample of starburst galaxies. We find that to explain the
deepest NIR upper limits assuming either a MW or SMC extinction law, a visual
extinction of AV > 50 is required, which is extremely unlikely. Since both GRBs
are bright in X-rays, explanation iii) also cannot explain their dark
classification, unless optical radiation and X-rays are not part of the same
synchrotron spectrum. An alternative, or complementary explanation of the
previous possibility, involves greyer extinction laws. A starburst attenuation
curve gives AV>10, which is less extreme, despite still very high. Assuming
high redshift in addition to extinction, implies an AV>10 at z=2 and AV>4-5 at
z=5, regardless of the adopted extinction recipe. A different, exotic
possibility would be an extremely high redshift origin (z>17 given the missing
K detections). Population III stars are expected to emerge at z ~ 20 and can
produce GRBs with energies well above those inferred for our GRBs at these
redshifts. Mid- and far-IR observations of these extreme class of GRBs can help
us to differentiate between the proposed scenarios.
