The spectra of mass-11 nuclei are unusual, and so pose a challenge for nuclear-structure theory. Relating to nucleon emission, the set of isobars range from being well-bound ($$^{11}$$
11
B,$$^{11}$$
11
C) through weakly bound ($$^{11}$$
11
Li, $$^{11}$$
11
Be), to being proton unstable ($$^{11}$$
11
N,$$^{11}$$
11
O). To add complexity, the weakly bound $$^{11}$$
11
Li takes the form of a two-nucleon halo nucleus. A self-consistent approach to understand this set of nuclei is especially important as the mirror pair $$^{11}$$
11
Be-$$^{11}$$
11
N exhibit a parity-inverted ground state compared to their neighboring nuclei. Herein, the Multi-Channel Algebraic Scattering method (MCAS) has been used to describe the low excitation spectra of those isobars in terms of nucleon-nucleus clusters. A collective model description of the low-excitation states of the mass-10 mass-10 core nuclei has been used to form the coupled-channel interactions required in the method. For comparison, and to understand the underlying configurations, a shell model approach has been used to obtain those spectra with no-core $$(0+2+4)\hbar \omega $$
(
0
+
2
+
4
)
ħ
ω
and $$(0+2)\hbar \omega $$
(
0
+
2
)
ħ
ω
shell-model spaces for the mass 10 and mass 11 nuclei respectively. The results of the calculations suggest the need of a strong coupling in the collective coupled-channel vibrational model. In particular, the strong coupling of the collective $$2^+_1$$
2
1
+
state of $$^{10}$$
10
Be to the valence neutron plays a decisive role in forming the positive parity ground state in $$^{11}$$
11
Be; an effect confirmed by the shell-model results.