After 30 Doradus, N11 is the second largest and brightest nebula in the Large Magellanic Cloud (LMC). This large nebula has several OB associations with bright nebulae at its surroundings. N11 was previously mapped at the lowest rotational transitions of ^12^CO (J=1-0 and 2-1), and in some particular regions, pointings of the ^13^ CO J=1-0 and 2-1 lines were also performed. Observationsof higher CO rotational transitions are needed to map gas with higher critical densities, which are useful to study the physical conditions of the gas component and its relation with the UV radiation more accurately. Using the Atacama Submillimeter Telescope Experiment, we mapped the whole extension of the N11 nebula in the ^12^CO J=3-2 line and three subregions in the ^13^CO J=3-2 line. The regions mapped in the ^13^CO J=3-2 were selected with the criterion that they were to be exposed to the radiation in different ways: a region lying across the nebula, which is related to the OB association LH10 (N11B), another region that it is associated with the southern part of the nebula, which is related to the OB association LH13 (N11D), and finally an area farther away in the southwest without any embedded OB association (N11I) We found that the morphology of the molecular clouds lying in each region shows some signatures that could be explained by the expansion of the nebulae and the action of the radiation. Fragmentation generated in a molecular shell due to the expansion of the N11 nebula is suggested. The integrated line ratios ^12^CO/^13^CO show evidence of selective photodissociation of the ^13^CO, and probably other mechanisms such as chemical fractionation. The values found for the integrated line ratios ^12^CO J=3-2/1-0 are in agreement with values that were assumed in previous works, and the CO contribution to the continuum at 870um was derived directly. The distribution of the integrated line ratios ^12^CO J=3-2/2-1 show indications of stellar feedback in N11B and N11D. The ratio between the virial and local thermal equilibrium (LTE) mass (M_vir_/M_LTE_) is higher than unity in all analyzed molecular clumps, which suggests that the clumps are not gravitationally bounded and may be supported by external pressure. A non-LTE analysis suggests that we map gas with densities of about a few 10^3^cm^-3^. The molecular clump at N11B, the unique molecular feature with direct evidence of ongoing star formation, is the densest of the clumps we analyzed.