Basically, you use 'sensitive' when it is related to sensations. For example, 'I have sensitive teeth so I can't drink cold water.' People can also be described as 'sensitive'. For example, a man who is in touch with his feminine side.
And you use 'sensible' when you are talking about a person or a decision which makes sense or is logical. Such as, 'He may be young but he is very sensible.' and 'It costs ten euro to take the bus and twenty euro to take the train. Both take the same length of time so the sensible decision would be to take the bus.'
As a general rule of thumb, items can not be 'sensible' and people can be both, depending on the situation.
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