Sensibility implies the capacity to feel. Most of us can react according to the ways in which we were miseducated to react; not as many of us, unfortunately, really (fully, independently) feel. Deep feeling usually does not take place when the mind is imprisoned in limited labels, categorizations, systems, and robotic practices. The aforementioned patterns tend to dull the mind, rendering it more programmed and less likely to feel. Psychological borders, such as those that take place between the observer and the observed, also tend to render dullness in the mind, making it far less likely for things like profound empathy to take place.
A truly intelligent mind that is beyond superficial borders, childish beliefs, and “learned patterns of separation,” may be capable of profound feeling (which is far beyond crass indifference).