There are \(n+m\) coins in a bag. In the bag \(n\) of them are fair (equal probability of outcomes) and \(m\) of them are double sided heads (heads on both sides).

The probability of picking a random coin and tossing it and getting heads is \(\frac{11}{17}\). Given that \(n\) and \(m\) are positive and that \(2n\le133+m\) work out how many different amounts of coins there could be.

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